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DOI: 10.4230/LIPIcs.SoCG.2022.17
URN: urn:nbn:de:0030-drops-160253
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16025/
Black, Mitchell ; Blaser, Nello ; Nayyeri, Amir ; Vågset, Erlend Raa
ETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth
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Abstract
Given a simplicial complex with n simplices, we consider the Connected Subsurface Recognition (c-SR) problem of finding a subcomplex that is homeomorphic to a given connected surface with a fixed boundary. We also study the related Sum-of-Genus Subsurface Recognition (SoG) problem, where we instead search for a surface whose boundary, number of connected components, and total genus are given. For both of these problems, we give parameterized algorithms with respect to the treewidth k of the Hasse diagram that run in 2^{O(k log k)}n^{O(1)} time. For the SoG problem, we also prove that our algorithm is optimal assuming the exponential-time hypothesis. In fact, we prove the stronger result that our algorithm is ETH-tight even without restriction on the total genus.
BibTeX - Entry
@InProceedings{black_et_al:LIPIcs.SoCG.2022.17,
author = {Black, Mitchell and Blaser, Nello and Nayyeri, Amir and V\r{a}gset, Erlend Raa},
title = {{ETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth}},
booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)},
pages = {17:1--17:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-227-3},
ISSN = {1868-8969},
year = {2022},
volume = {224},
editor = {Goaoc, Xavier and Kerber, Michael},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16025},
URN = {urn:nbn:de:0030-drops-160253},
doi = {10.4230/LIPIcs.SoCG.2022.17},
annote = {Keywords: Computational Geometry, Surface Recognition, Treewidth, Hasse Diagram, Simplicial Complexes, Low-Dimensional Topology, Parameterized Complexity, Computational Complexity}
}
| Keywords: | Computational Geometry, Surface Recognition, Treewidth, Hasse Diagram, Simplicial Complexes, Low-Dimensional Topology, Parameterized Complexity, Computational Complexity | |
| Seminar: | 38th International Symposium on Computational Geometry (SoCG 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 01.06.2022 |
